Student will understand that not all elements in a data set are equally likely.
Student will know the following terms, expected value, probability, events, sets, mean, relative frequency, compound and combinations. Students will also know the formulas for probability and expected value.
Student will be able to solve for the expected value of a data set.
Maine Learning Results Alignment
Maine Learning Result: Mathematics - B. Data
Probability
Grade 9 - Diploma
5. Students understand the relationship of probability to relative frequency and know how to find the probability of compound events.
b. Find expected value of events
Assessment
Formative (Assessment for Learning)
The students will be completing a guided practice worksheet for calculating expected value. This will be given after the lecture portion of the class. The teacher will put 2 problems on the board (see teacher notes) for the students to practice individually. While the students are working on these problems the teacher will be walking around the room observing how the students are doing with the problems.
Summative (Assessment of Learning)
Students will be given an in class activity in which they will use a "dice simulator" to explore expected value. The students will need to complete the worksheet associated with the activity, which will be graded on completeness. If the students complete the activity then they will have achieved the understanding of the lesson. The students will simulate the rolling of two dice and record their data into a table. They will then calculate the expected value of rolling two dice and see how their simulation results match their expected value calculations.
Integration
Technology: Students will view a commercial for Monopoly as part of the hook. The students will also use a "dice simulator" to complete their activity for the lesson.
English: Students will be reading and recording data as part of research to understanding expected value.
Art: The students will have the option to create a visual for their data researched as a continuation of what they learned about in lesson three.
Groupings
Students will be broken up in pairs based on shirt color. Each student must find one other student with the same colored shirt to be partners with. Any students without partners for one reason or another can just be randomly assigned together at the instructors discretion. This activity will be easy fairly straightforward to do, so no matter who gets partnered with who the activity should be able to be completed.
Differentiated Instruction
Strategies Mathematical/Logical: Students will be compiling data and calculating probabilities. Interpersonal: Students will be working in groups and discussing material. Spatial/Visual: Students will be viewing a video and using the internet to research. Musical: Students will be able to include sound and music in their presentations. Music will also be played during class work time. Verbal/Linguistic: Students will be discussing their ideas in groups. Intrapersonal: Students will be working alone on their quizzes.
Modifications/Accommodations
I will review students' IEPs, 504s, ELLIDEPs and make the appropriate modifications and accommodations for students. All subject matter will be appropriate for everyone, the only forseeable issue may arise for students with colorblindness and if that is the case those students will be able to get aid from another classmate or instructor to differentiate colors.
Absent Students: Students who miss the class with an excused absence they will be required to make up the in class activity, either on their own or with another absent student. The absent students are encouraged to see the teacher for notes and any other information that was included in this lesson. Since the only graded work from this lesson is the in class activity, then absent students (and all students for that matter) will be allowed the option of extra practice problems for calculating expected value.
Extensions
All students will be able to relate to the Monopoly commercial (unless they have not played it!) to be familiar with the application of expected value included in the activity is done in class. All studens will also use a "dice simulator" on their laptop to speed up the process of collecting raw data for the class activity. This will allow students to apply modern technology to the mathematics they will be using in class.
Materials, Resources and Technology
Teacher Notes
Activity Table
Deal or No Deal Game
Activity Worksheet
Laptops
Projector
Dice Simulator
Deal or No Deal Blog
Maine Standards for Initial Teacher Certification and Rationale
Standard 3 - Demonstrates a knowledge of the diverse ways in which students learn and develop by providing learning opportunities that support their intellectual, physical, emotional, social, and cultural development. Rationale: This lesson meets the Maine Standards for Initial Teacher Certification by allowing students multiple approaches to learning the material of expected value. The students will be able to learn about expected value through a short lecture introducing the concepts and formula. The students will then get a chance to practice these skills by participating in some guided practice. This will allow the students to try out this new concept in a neutral atmosphere. The students will then be able to apply what they know, and express it through their favorite or a notable athlete, by completing the activity in class with their group. The members of the group will help each other in the learning process by answering and getting help with questions.
Standard 4 - Plans instruction based upon knowledge of subject matter, students, curriculum goals, and learning and development theory. Rationale: The learning of expected value will come in this lesson. The previous lessons will have built up the students skills to compute probabilities of any kind. Expected value is an extension of calculating probabilities so it must be taught after the students know and understand how to calculate and compound probabilities. This lesson will also reinforce topics discussed in the previous class of how elements are not all weighted the same in a data set.
Standard 5 - Understands and uses a variety of instructional strategies and appropriate technology to meet students’ needs. Rationale: The students will be taught through a lecture as well as an activity. The lecture will open with the hook for the class which will be viewing a Monopoly commercial. This commercial will set the stage for the activity to be completed after the lecture. It will be a good way for students to get thinking about where they can apply the concepts they will be learning about. The students will then use a computer program that simulates the rolling of dice. This will aide in the students activity when it comes time for them to do the research required for the activity in class.
Standard 8 - Understands and uses a variety of formal and informal assessment strategies to evaluate and support the development of the learner. Rationale: The students will be given two different assessments to check for the understanding of the material. The students will first be given some practice problems right after the lecture portion of the class. This will allow the students and teacher to see right away where everyone is in the learning process. The students will then be graded over a class activity applying the concepts of expected value learned in lecture. The activity will help the students explore how to use expected value in the real world.
Teaching and Learning Sequence:
(0-15 minutes) The students will walk into the classroom and find the desks in rows facing the front of the classroom. The students will all take their seats and find the following agenda written on the left side of the chalkboard.
Today's Agenda
1. Welcoming (0-15)
a. Homework Review/Blogs
b. Recap from Last Time
c. Deal or No Deal
2. Lecture (15-35)
a. Vocabulary
b. Expected Value and Examples
c. Try It on Your Own
3. Pretend Dice Rolling (35-65)
a. Groups by Color
b. Research
c. Complete Worksheet
4. Conclusion (65-80)
a. Recap
b. Last Questions
c. What up Next?
Once the students have all found their seats, they will see the agenda and know to take a laptop out and load up their blog entries assigned with their homework from the previous class. The students will also take their homework out and be ready to go over it as a class. The students will be given the opportunity to refer tot heir blog entries and ask questions they had over the homework. The teacher will answer any questions before moving on with the lesson. Once that has happened the students will then learn about how what they have already learned will be applied to this lesson. This is because the students have been learning to calculate probabilities will which will be used to calculate expected value. This will be explained as followed, expected value tells you what you can expect to be the most likely outcome for a set of data. This will lead into the hook for the lesson which will be a about the game show “Deal or No Deal” (http://www.nbc.com/Deal_or_No_Deal/game/). Before playing the game with the class, have each student bring up the blog on “Deal or No Deal” onto their laptops and have them read the entire blog. This should not take any more than a few minutes. This is relevant because the students will be calculating expected values later on in class, and this concept is directly tied into “Deal or No Deal”. As a class we will play a round of “Deal or No Deal” and talk about the banker offers and how he might come up with them. Studies have been done by students at UMF, and they have found that the best offer that a contestant can get is when the banker offer matches the expected value for the round. This usually happens near the middle of the game. You can calculate the expected value of any round by adding up all of the dollar amounts left in the round and dividing by the total number of cases left. Where, What, Why, Hook. Tailor: Mathematical/Logical, Linguistic, Intrapersonal, Interpersonal
(15-35 minutes) After the hook has happened, the students will then take notes over Expected Value. The first to be discussed will be all new vocabulary and reviewing any previous vocabulary for this material. This is important because students need to know what the words mean that they will be dealing with for the rest of the lesson (See teacher notes). The teacher will then introduce the formula for expected value and what it is. Expected value is when you sum up all of the (events times their probability) to arrive at a value. Refer to the teacher notes for examples. The students will see at least two examples of how to calculate expected value. After this has happened, the students will then get the opportunity to try out the new material on their own, as part of a guided practice. The teacher should put two examples on the chalkboard for the students to do. (These examples can be found in the teacher notes). While the students are working on these problems the teacher will be walking around the room taking note to how the students are dong with the material. The students should feel free to ask the teacher any questions they may have with the material. After the students complete the problems they will ask any questions over them before the activity portion of the class is started. Equip, Tailor: Musical, Interpersonal, Intrapersonal, Mathematical/Logical, Spatial
(35-65 minutes)After the lecture portion of the class has ended the students will be asked to all stand up and line up against the wall. They will then be instructed to find another student with the same shirt color to be partners with. If there are a few students left out of finding partners, they should be partnered together. Once partners have been assigned the students will put pair up their desks. The students will need to have their laptop out (at least one laptop per pairing). While the students are getting situated the teacher will be passing out the activity (See Teacher Notes). There will be a sheet with directions and a table on if for the students to use. The activity will have the students (in their pairs) using the "Dice Simulator" to simulate the rolling of two dice. Each pair of students should gather 50+ pieces of data, (Using the program this will not be hard to accomplish). Once they have gathered all of this data into their table they should calculate the probability of each sum happening by using the formula for probability. Once they have done this the students will then decide what sum of the dice they expect to be the expected value of the data set. Once they have done this the students will then calculate the expected value for the sum of rolling two dice and see how their prediction faired. After this the students (as a whole class) will compile all of their information they gathered and see how close their individual results match the overall class results. This is important because the more elements in the data set, the better picture one can get for the probability. Explore, Re-think, Revise, Tailor: Mathematical/Logical, Spatial, Interpersonal, Intrapersonal, Musical, Linguistic
(65-80 minutes)After the activity has been completed the students will then recap the class material with the instruction of the teacher. They will review what expected value is, why it is used and how it related to the previous material learned. The students will then have the opportunity to ask any final questions before the end of class. Once this has happened the teacher will then talk to the students about what they will be learning about next time. During the next lesson the students will be using their knowledge of probability, graphs and expected value to create their own problems and solve them in groups. This will help them truly master the material. Evaluate, Tailor: Intrapersonal, Interpersonal, Mathematical/Logical
UMF LESSON PLAN FORMAT
Teacher’s Name: Mr. Hart Lesson # : 4
Grade Level: 9-Diploma Topic: Expected Value
Objectives:
Maine Learning Results Alignment
Probability
Grade 9 - Diploma
5. Students understand the relationship of probability to relative frequency and know how to find the probability of compound events.
b. Find expected value of events
Assessment
The students will be completing a guided practice worksheet for calculating expected value. This will be given after the lecture portion of the class. The teacher will put 2 problems on the board (see teacher notes) for the students to practice individually. While the students are working on these problems the teacher will be walking around the room observing how the students are doing with the problems.
Students will be given an in class activity in which they will use a "dice simulator" to explore expected value. The students will need to complete the worksheet associated with the activity, which will be graded on completeness. If the students complete the activity then they will have achieved the understanding of the lesson. The students will simulate the rolling of two dice and record their data into a table. They will then calculate the expected value of rolling two dice and see how their simulation results match their expected value calculations.
Integration
English: Students will be reading and recording data as part of research to understanding expected value.
Art: The students will have the option to create a visual for their data researched as a continuation of what they learned about in lesson three.
Groupings
Differentiated Instruction
Mathematical/Logical: Students will be compiling data and calculating probabilities.
Interpersonal: Students will be working in groups and discussing material.
Spatial/Visual: Students will be viewing a video and using the internet to research.
Musical: Students will be able to include sound and music in their presentations. Music will also be played during class work time. Verbal/Linguistic: Students will be discussing their ideas in groups.
Intrapersonal: Students will be working alone on their quizzes.
I will review students' IEPs, 504s, ELLIDEPs and make the appropriate modifications and accommodations for students. All subject matter will be appropriate for everyone, the only forseeable issue may arise for students with colorblindness and if that is the case those students will be able to get aid from another classmate or instructor to differentiate colors.
Absent Students: Students who miss the class with an excused absence they will be required to make up the in class activity, either on their own or with another absent student. The absent students are encouraged to see the teacher for notes and any other information that was included in this lesson. Since the only graded work from this lesson is the in class activity, then absent students (and all students for that matter) will be allowed the option of extra practice problems for calculating expected value.
All students will be able to relate to the Monopoly commercial (unless they have not played it!) to be familiar with the application of expected value included in the activity is done in class. All studens will also use a "dice simulator" on their laptop to speed up the process of collecting raw data for the class activity. This will allow students to apply modern technology to the mathematics they will be using in class.
Materials, Resources and Technology
Activity Table
Deal or No Deal Game
Activity Worksheet
Laptops
Projector
Dice Simulator
Deal or No Deal Blog
Source for Lesson Plan and Research
Deal or No Deal Game
(http://www.nbc.com/Deal_or_No_Deal/game/)
Dice Simulator made by Jesse and Nick Hart
(http://students.umf.maine.edu/~hartna)
Deal or No Deal Blog
(
http://pinchak.blogspot.com/2005/12/deal-or-no-deal-its-all-about-expected.html)
Maine Standards for Initial Teacher Certification and Rationale
Rationale: This lesson meets the Maine Standards for Initial Teacher Certification by allowing students multiple approaches to learning the material of expected value. The students will be able to learn about expected value through a short lecture introducing the concepts and formula. The students will then get a chance to practice these skills by participating in some guided practice. This will allow the students to try out this new concept in a neutral atmosphere. The students will then be able to apply what they know, and express it through their favorite or a notable athlete, by completing the activity in class with their group. The members of the group will help each other in the learning process by answering and getting help with questions.
Rationale: The learning of expected value will come in this lesson. The previous lessons will have built up the students skills to compute probabilities of any kind. Expected value is an extension of calculating probabilities so it must be taught after the students know and understand how to calculate and compound probabilities. This lesson will also reinforce topics discussed in the previous class of how elements are not all weighted the same in a data set.
Rationale: The students will be taught through a lecture as well as an activity. The lecture will open with the hook for the class which will be viewing a Monopoly commercial. This commercial will set the stage for the activity to be completed after the lecture. It will be a good way for students to get thinking about where they can apply the concepts they will be learning about. The students will then use a computer program that simulates the rolling of dice. This will aide in the students activity when it comes time for them to do the research required for the activity in class.
Rationale: The students will be given two different assessments to check for the understanding of the material. The students will first be given some practice problems right after the lecture portion of the class. This will allow the students and teacher to see right away where everyone is in the learning process. The students will then be graded over a class activity applying the concepts of expected value learned in lecture. The activity will help the students explore how to use expected value in the real world.
Teaching and Learning Sequence:
Today's Agenda
1. Welcoming (0-15)
a. Homework Review/Blogs
b. Recap from Last Time
c. Deal or No Deal
2. Lecture (15-35)
a. Vocabulary
b. Expected Value and Examples
c. Try It on Your Own
3. Pretend Dice Rolling (35-65)
a. Groups by Color
b. Research
c. Complete Worksheet
4. Conclusion (65-80)
a. Recap
b. Last Questions
c. What up Next?
Once the students have all found their seats, they will see the agenda and know to take a laptop out and load up their blog entries assigned with their homework from the previous class. The students will also take their homework out and be ready to go over it as a class. The students will be given the opportunity to refer tot heir blog entries and ask questions they had over the homework. The teacher will answer any questions before moving on with the lesson. Once that has happened the students will then learn about how what they have already learned will be applied to this lesson. This is because the students have been learning to calculate probabilities will which will be used to calculate expected value. This will be explained as followed, expected value tells you what you can expect to be the most likely outcome for a set of data. This will lead into the hook for the lesson which will be a about the game show “Deal or No Deal” (http://www.nbc.com/Deal_or_No_Deal/game/). Before playing the game with the class, have each student bring up the blog on “Deal or No Deal” onto their laptops and have them read the entire blog. This should not take any more than a few minutes. This is relevant because the students will be calculating expected values later on in class, and this concept is directly tied into “Deal or No Deal”. As a class we will play a round of “Deal or No Deal” and talk about the banker offers and how he might come up with them. Studies have been done by students at UMF, and they have found that the best offer that a contestant can get is when the banker offer matches the expected value for the round. This usually happens near the middle of the game. You can calculate the expected value of any round by adding up all of the dollar amounts left in the round and dividing by the total number of cases left. Where, What, Why, Hook. Tailor: Mathematical/Logical, Linguistic, Intrapersonal, Interpersonal